V. Yu. Petrov

A Chiral Theory of Nucleons

Abstract We present arguments that QCD at low momenta is reduced to a simple theory given by a path integral over pion fields and quarks which obtain dynamical mass owing to chiral symmetry breaking. The dimensional quantities of this low-momenta theory are fixed through the ΛQCD parameter. The effective chiral lagrangian is given by a quark determinant in a background chiral field. Its properties are investigated both for slowly and rapidly varying pion fields. Though it satisfies requirements known from theory and phenomenology, it does not possess non-trivial soliton solutions. However we show that, at large Nc, nucleons correspond not to the local minimum of the effective chiral lagrangian but to a minimum of a more subtle quantity. In general, different functionals of the chiral field should be minimized, depending on the baryon charge of the system. We obtain a quantitative picture of nucleons as localized states of “constituent” quarks bound by a self-consistent pion field. Its properties, such as electromagnetic form factors, etc., are investigated in detail. We get very reasonable numerical values for the nucleon static properties.

Off - forward quark distributions of the nucleon in the large N(c) limit

We study the off-forward quark distributions (OFQDs) in the chiral quark-soliton model of the nucleon. This model is based on the large-

Unpolarized and polarized quark distributions in the large N(c) limit

{N}_{c}

Pion and photon light cone wave functions from the instanton vacuum

picture of the nucleon as a soliton of the effective chiral Lagrangian and allows one to calculate the leading twist quark and antiquark distributions at a low normalization point. We demonstrate the consistency of the approach by checking various sum rules for the OFQDs. We present numerical estimates of the isosinglet distribution

A formula for the Wilson loop

H(x,\ensuremath{\xi},{\ensuremath{\Delta}}^{2})

Nucleon mass and nucleon sigma term

. In contrast with other approaches we find a strong qualitative dependence on the longitudinal momentum transfer,

Yang-Mills theory in three dimensions as a quantum gravity theory

\ensuremath{\xi}

Mesomolecule formation in tμ + HD(D2) reactions

. In particular,

The Wilson loop and heavy-quark potential in the instanton vacuum

H(x,\ensuremath{\xi},{\ensuremath{\Delta}}^{2})

Non-Abelian Stokes theorems in the Yang-Mills and gravity theories

as a function of